Symbolic Computation of Local Symmetries of Nonlinear and Linear Partial and Ordinary Differential Equations

The paper illustrates the use of a symbolic software package GeM for Maple to compute local symmetries of nonlinear and linear differential equations (DEs). In the cases when a given DE system contains arbitrary functions or parameters, symbolic symmetry classification is performed. Special attention is devoted to the computation of point symmetries of linear PDE systems. Routines are available that effectively eliminate infinite obvious symmetries of linear DEs.